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<h2 class="hd hd-2 unit-title">Problem 2.1</h2>
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Problem 9.1
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<b>Part A</b>
<p>Several types of magnetic devices, including transformers, electromagnets, and hard disk write heads, consist of a current-carrying coil wrapped around a magnetic core (or pole piece). Indicate which properties the material in the magnetic core should have:</p>
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<b>Part B</b>
<p>Estimate how much magnetic field an electromagnet can produce at its gap, \(H_g\). Assume that the pole-piece is horseshoe-shaped, with a total length of \(1 m\), and the gap is \(10 cm\) long. The pole-piece is wrapped by \(500\) turns of wire which carry \(i = 1 A\). The pole-piece has \(\mu _r = 1000 \) and \(B_s = 0.5 T\). You can assume that \(B_g \approx B_c\) and that under these conditions the core does not saturate.</p>
<p>\(H_g\) (in kA/m):</p>
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<p>What would happen to the gap field \(H_g\) if the current \(i\) increases to \(100 A\)?</p>
<p>\(H_g\) (in kA/m):</p>
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<h2 class="hd hd-2 unit-title">Problem 2.2</h2>
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Problem 2.2
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<p>A microphone consists of a paper cone with a magnet attached at its center. The magnet hangs above a coil of wire through which current flows. (See diagram below) When sound hits the paper cone, it moves the magnet. This creates a changing magnetic field within the coil which produces a voltage across the wire. This voltage pattern, over time, is the recording of the sound.</p>
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<p>If the magnet is \(1 mm^{2}\) in cross-section and is made from a material with \(B_s = 1 T\), and the coil has 100 turns, calculate the magnetic flux \(\Phi\) that can be contained within the magnetic core. </p>
<p>\(\Phi\) (in Wb):</p>
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<p> What is the magnitude of the signal, in volts, that you could expect from the microphone? Assume that we get a maximum signal when the flux varies from \(0\) to the value of \(\Phi\) calculated above. (Assume that sound has a frequency of order \(500 Hz\).)</p>
<p>Voltage (in \(V\)):</p>
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